Small beer is a beer that contains very little alcohol, perhaps less than one percent. Sometimes unfiltered and porridge-like, it was a favored drink in Medieval Europe and colonial North America. It was sometimes had with breakfast, as attested in Benjamin Franklin's autobiography. Before public sanitation, water-transmitted diseases, such as cholera, were a significant cause of death. Because alcohol is toxic to most water-borne pathogens, and because the process of brewing any beer from malt involves boiling the water, which also kills them, drinking small beer instead of water was one way to escape infection.
Small beer can also refer to a beer made of the "second runnings" from a very strong beer (e.g., scotch ale) mash. These beers can be as strong as a mild ale, depending on the strength of the original mash. This was done as an economy measure in household brewing in England up to the 18th century and is still done by some homebrewers.
Small beer is not made in any significant amount today, though a similar product called non-alcoholic beer (which actually has a little alcohol) is quite common.
Metaphorically, small beer means a trifle, a thing of little importance.